Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces
Provides theoretical optimality guarantees for regularization methods, benefiting researchers in inverse problems and functional analysis.
The paper proves optimal convergence rates for regularization methods solving linear ill-posed operator equations in Hilbert spaces, generalizing existing results to general source conditions including logarithmic ones, and establishing optimality under variational source conditions.
In this paper, we prove optimal convergence rates results for regularisation methods for solving linear ill-posed operator equations in Hilbert spaces. The result generalises existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions.